Vice President Joe Biden is leading the gun-control task force and also recently sealed the fiscal-cliff deal. It's possible that his old-school, backslapping style of politicking may be coming back in vogue.

Vice President Joe Biden, with Attorney General Eric Holder (l.), speaks during a meeting with victims' groups and gun-safety organizations in the Eisenhower Executive Office Building in the White House complex Wednesday.

This week, he's heading up the gun-control talks at the White House, bringing all parties to the table and, in typical Biden fashion, making news with his declaration Wednesday that the president would consider using executive orders to make something happen.

The vice president also proved pivotal in the recent "fiscal cliff" negotiations, almost single-handedly sealing a deal with Republicans at the 11th hour. As Major Garrett writes in National Journal this week, Mr. Biden "made or took 13 calls from Senate GOP Leader Mitch McConnell of Kentucky during the weekend that most cliff issues were resolved." He added, "Can anyone imagine President Obama calling anyone about anything 13 times?" It was a reprising of the dealmaking role that Biden played in 2011's debt-ceiling negotiations.

Mr. Garrett pointedly calls Biden a "closer" – the only one the administration has. Notably, Ezra Klein uses the same term in his Bloomberg column this week, in which, like Garrett, he describes Biden as an underrated legislator and politician, "the White House closer, the guy who can cut a deal with the Republicans after everyone else has failed."

Mr. Klein goes on to note that Biden's off-the-cuff remarks often provide "comic relief" – and, as a result, his presidential ambitions have been mostly "laughed off." But in fact, the prospect of a Biden 2016 campaign is something we should take quite seriously.

That's a far cry from the general consensus among the chattering classes not too long ago, when most Democratic insiders were tending to play down, if not completely write off, Biden's chances. And it may still be a bit optimistic.

As U.S. News & World Report's Ken Walsh writes: "Americans in recent years have mostly elected Washington outsiders or fresh faces to the presidency, such as Obama, George W. Bush, and Bill Clinton. Being a Washington insider such as Biden no longer has much appeal in either major party."

But the recent health scare and hospitalization of Hillary Rodham Clinton, who's been widely regarded as the Democratic front-runner should she decide to enter the fray (though she's hardly a fresh face, either) has added a touch more uncertainty to the 2016 field. If Mrs. Clinton decides in the end not to run, then it becomes a wide-open race – with Biden's chances to win the nomination as good or better than anyone else's.

And it's possible that Biden's old-school, backslapping style of politicking may be coming back in vogue – in part because it stands as such a sharp contrast to what has become the chief criticism of his boss: the widespread lament, even from many Democrats, that Mr. Obama is too "aloof," "condescending," and generally too above-it-all to dirty his hands in the Washington mud pit.

That's why the image of Biden as a "closer" is a shrewd one for the veep's aides to circulate now – since it speaks to the general longing for Washington to get things done. Their guy may not be the flashy starting pitcher, as the analogy goes, but he's the one who ultimately wins the game.

It's true that Americans don't like the way Beltway politics are played. But electing someone who's reluctant to join the game can lead to nothing happening at all. With Washington gridlock seeming more and more intractable – even as the challenges facing the nation become more and more pressing – an old-fashioned dealmaker in chief like Biden may seem like just what the country needs.